Cremona's table of elliptic curves

5082 = 2 · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	5082bb	Isogeny class
Conductor	5082	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-89625989376 = -1 · 28 · 310 · 72 · 112	Discriminant
Eigenvalues	2- 3- -3 7- 11- -3  5 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1152,20736]	[a1,a2,a3,a4,a6]
Generators	[-18:198:1]	Generators of the group modulo torsion
j	-1397395501513/740710656	j-invariant
L	5.7231634389367	L(r)(E,1)/r!
Ω	0.9985470464819	Real period
R	0.035821818931195	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40656bn1 15246w1 127050g1 35574ce1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082bb1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-3	-	-	-3	5	-6	-4	-3	-2	1	-11	10	-6	-1	-6	-10	8	-2	6	-14	8	3	-15

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Quadratic twists for elliptic curve 5082bb1

-4	-3	5	-7	-11
40656bn1	15246w1	127050g1	35574ce1	5082k1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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